Timeline for Inverse of holomorphic elliptic differential operator
Current License: CC BY-SA 4.0
8 events
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| May 19, 2018 at 8:04 | comment | added | Peter Michor | Using a resolvent integral along a simple closed curve containing some eigenvalues in the interior you can reduce the question to the finite dimensional matrix case. So Igor Khavkine's comment precisely answers your question. | |
| S May 19, 2018 at 6:56 | history | suggested | CommunityBot | CC BY-SA 4.0 |
minor spelling fix for title
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| May 19, 2018 at 2:16 | review | Suggested edits | |||
| S May 19, 2018 at 6:56 | |||||
| May 18, 2018 at 7:32 | answer | added | Guest | timeline score: 1 | |
| May 18, 2018 at 5:36 | comment | added | Igor Khavkine | If you replace $\Delta$ by some finite dimensional matrix, not necessarily symmetric/hermitian, then higher order poles of $A(z)^{-1}$ correspond to higher order Jordan blocks in the canonical form of $\Delta$. If you do the calculation explicitly for $\Delta$ being a single Jordan block, you'll see where the higher order singularities appear. | |
| May 17, 2018 at 23:05 | comment | added | Christian Remling | $\langle f, (A-z)^{-1} f\rangle$ has positive imaginary part in the upper half plane for any self-adjoint $A$, so possible real poles must be of order $1$. | |
| May 17, 2018 at 19:21 | history | edited | Slm2004 | CC BY-SA 4.0 |
deleted 4 characters in body
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| May 17, 2018 at 18:36 | history | asked | Slm2004 | CC BY-SA 4.0 |